How to make a logo cycle (or loop) on top of a clip in movie editing mode?
Seems like there is no option to make an image sequence loop in within the VSE.

A workaround is loading your image sequence in the compositor, making sure you have the cyclic option enabled:
(in this example is an image sequence of 11 frames with alpha channel)



Then add a Scene strip to the VSE, make it alpha over, and disable OpenGL preview in the Scene Preview/Render, so you get the image sequence from the compositor. The 11 frames will play repeatedly the duration of the scene strip.